Preliminary report with traditional stability, Effect of climatic extremes on community stability and its drivers
Shyamolina Ghosh, Owen Petchey
01 April, 2024
1 Introduction
2 Data
2.1 Data structure
Total 1947 community timeseries we have collected for the timespan 1979-2019. 4 taxa are considered - birds, fish, freshwater invertebrates, terrestrial invertebrates. Below is the summary of the datatable. Description of each column is given in README.txt
## 'data.frame': 1947 obs. of 63 variables:
## $ source : chr "BioTIME" "BioTIME" "BioTIME" "BioTIME" ...
## $ STUDY_ID : chr "57" "229" "229" "229" ...
## $ newsite : chr "57" "STUDY_ID_229_LAT35.04016_LON-83.36127" "STUDY_ID_229_LAT35.11187_LON-83.39091" "STUDY_ID_229_LAT35.14137_LON-83.29577" ...
## $ REALM : chr "Freshwater" "Freshwater" "Freshwater" "Freshwater" ...
## $ TAXA : chr "fish" "fish" "fish" "fish" ...
## $ ORGANISMS : chr "fish" "fish" "fish" "fish" ...
## $ initR : int 76 24 30 32 25 37 22 30 26 31 ...
## $ nsp : int 34 14 11 17 14 16 13 11 14 10 ...
## $ nyr_used : int 32 23 20 21 21 23 23 20 20 28 ...
## $ startyr : int 1981 1990 1990 1991 1990 1990 1990 1995 1995 1979 ...
## $ endyr : int 2012 2013 2013 2012 2013 2013 2013 2014 2014 2006 ...
## $ nint : int 561 91 55 136 91 120 78 55 91 45 ...
## $ nind : int 503 59 35 97 61 91 67 46 60 36 ...
## $ npos : int 35 29 20 27 29 27 11 7 26 7 ...
## $ nL : int 24 21 13 9 3 14 3 3 15 7 ...
## $ nU : int 11 8 7 18 26 13 8 4 11 0 ...
## $ nneg : int 23 3 0 12 1 2 0 2 5 2 ...
## $ L : num 3.027 2.557 1.046 1.028 0.267 ...
## $ U : num -1.252 -0.633 -0.49 -2.547 -2.938 ...
## $ f_nind : num 0.897 0.648 0.636 0.713 0.67 ...
## $ f_nL : num 0.0428 0.2308 0.2364 0.0662 0.033 ...
## $ f_nU : num 0.0196 0.0879 0.1273 0.1324 0.2857 ...
## $ f_nneg : num 0.041 0.033 0 0.0882 0.011 ...
## $ cvsq_real : num 1.565 0.189 0.239 0.11 0.158 ...
## $ cvsq_indep : num 1.5001 0.0963 0.0879 0.0475 0.1099 ...
## $ phi : num 1.04 1.96 2.72 2.33 1.44 ...
## $ phi_LdM : num 0.454 0.552 0.388 0.442 0.542 ...
## $ skw_real : num 5.172 0.363 0.505 2.41 -0.296 ...
## $ skw_indep : num 5.064 0.612 0.737 0.841 -0.877 ...
## $ phi_skw : num 1.021 0.593 0.685 2.866 0.337 ...
## $ iCV : num 0.799 2.303 2.045 3.008 2.512 ...
## $ iCValt : num 1.81 1.9 1.56 3.7 2.15 ...
## $ LONGITUDE : num -89.5 -83.4 -83.4 -83.3 -83.5 ...
## $ LATITUDE : num 44 35 35.1 35.1 35.2 ...
## $ t_med : num 2809 2865 2868 2864 2864 ...
## $ t_skw : num 0.4478 0.1228 0.158 -0.0283 0.0353 ...
## $ t_var : num 0.00401 0.00228 0.00208 0.00233 0.00239 ...
## $ t_kurt : num 3.18 2.33 2.27 2.55 2.39 ...
## $ t_varIQR : num 11.27 6.54 5.98 6.67 6.83 ...
## $ t.lm.slope : num 0.341 0.258 0.106 0.365 0.2 ...
## $ t.lm.slope.sig : int 1 0 0 0 0 0 0 0 0 0 ...
## $ t.sens.slope : num 0.333 0.333 0.215 0.448 0.319 ...
## $ t.sens.slope.sig : int 0 0 0 0 0 0 0 0 0 0 ...
## $ t_med_celsius : num 7.77 13.31 13.67 13.23 13.2 ...
## $ t_skw_celsius : num 0.4478 0.1228 0.158 -0.0283 0.0353 ...
## $ is.sig_t_skw_celsius : int 0 0 0 0 0 0 0 0 0 0 ...
## $ t_var_celsius : num 0.145 0.0492 0.0438 0.0504 0.0518 ...
## $ t_kurt_celsius : num NA NA NA NA NA NA NA NA NA NA ...
## $ is.sig_t_kurt_celsius : int NA NA NA NA NA NA NA NA NA NA ...
## $ t_varIQR_celsius : num 1.127 0.654 0.598 0.667 0.683 ...
## $ t.lm.slope.celsius : num 0.0341 0.0258 0.0106 0.0365 0.02 ...
## $ t.lm.slope.sig.celsius : int 1 0 0 0 0 0 0 0 0 0 ...
## $ t.sens.slope.celsius : num 0.0333 0.0333 0.0215 0.0448 0.0319 ...
## $ t.sens.slope.sig.celsius: int 0 0 0 0 0 0 0 0 0 0 ...
## $ is.stationary.adf : int 0 1 1 0 1 1 1 1 1 0 ...
## $ is.trend.stationary.kpss: int 0 0 0 0 0 0 0 0 0 0 ...
## $ GiniSimpson : num 0.817 0.57 0.92 0.819 0.521 ...
## $ Simpson : num 0.142 0.152 0.555 0.256 0.138 ...
## $ Shannon : num 0.67 0.512 0.863 0.695 0.471 ...
## $ Heip : num 0.291 0.22 0.693 0.385 0.19 ...
## $ McIntosh : num 0.658 0.428 0.852 0.688 0.384 ...
## $ SmithWilson : num 0.415 0.35 0.627 0.315 0.325 ...
## $ Pielou : num 0.19 0.194 0.36 0.245 0.178 ...3 Methods
Figure 3.1: Temperature timeseries figure with real data
3.1 Variables estimated and modelled
(Perhaps make this into a table.)
Let \(N_{i,t,s}\) be the abundance (sometimes it was biomass data when abundance data were not available) of species \(i\) at time \(t\) at site \(s\). Total abundance at time \(t\) at site \(s\) is \(N_{t,s} = \sum_{i=1}^{s} N_{t,s,i}\).
Community stability at site \(s\) was estimated as the inverse of the coefficient of temporal variation in total community abundance (when abundance info were not available, then biomass): \(TempStab_s = 1 / CV(N_{t,s}) = abs(mean(N_{t,s})) / sd(N_{t,s})\)
Species richness at site \(s\) was estimated as the number of total species (\(nsp\)) and dominant species that were present minimum 70% of the total years sampled (\(R\)).
Species evenness at site \(s\) was estimated as Smith-Wilson matrix.
Community variance ratio: a measure of synchrony, scaled between 0 to 1 (Loreau & Mazancourt).
Community level total tail association from pairwise synchrony: see BioDyn project, Figure 1.
Temperature median: Median of CHELSA-extracted annual temperature timeseries for the study years included in the analysis for each community.
Temperature trend: Monotonic trend of annual temperature timeseries (computed by non-parametric Sen’s method or parametric linear fit slope). I used the Sen’s slope in the path model, as non-parametric estimation has some advantage, see wikipedia, but it is very similar to linear slope (see 4.24).
Temperature skew: Skewness of CHELSA-extracted annual temperature timeseries for the study years included in the analysis for each community.
Temperature variability: Temperature variability for the community during the study period = IQR(annual temperature distribution for the study period).
4 Results
4.1 Community stability exploration
Figure 4.1: Stability-diversity relationship for birds and fish.
4.1.1 Birds
Figure 4.2: Stability-diversity relationship for birds at different temperature levels
Figure 4.3: Stability-temperature relationship for bird communities at different richness levels
Figure 4.4: Stability-synchrony relationship for birds at different temperature levels
Figure 4.5: Synchrony-temperature relationship (scatterplot)
Figure 4.6: Synchrony-temperature relationship (boxplot)
Figure 4.7: Synchrony richness relationship.
Figure 4.8: Synchrony temperature relationship.
Figure 4.9: Stability - temperature skew relationship.
Figure 4.10: Stability - temperature skew relationship.
Figure 4.11: Stability - temperature skew relationship.
Figure 4.12: Stability - temperature skew relationship.
4.1.1.1 Basic statistics for birds
Model of bird stability:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 4.3009 | 0.4507 | 9.5429 | 0.0000 |
| nsp | 0.0315 | 0.0107 | 2.9469 | 0.0033 |
| t_med_celsius | -0.1413 | 0.0370 | -3.8197 | 0.0001 |
| nsp:t_med_celsius | 0.0034 | 0.0009 | 3.8206 | 0.0001 |
Model of bird synchrony:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 0.2954 | 0.0218 | 13.5237 | 0.0000 |
| nsp | -0.0027 | 0.0005 | -5.2091 | 0.0000 |
| t_med_celsius | 0.0033 | 0.0018 | 1.8185 | 0.0692 |
| nsp:t_med_celsius | -0.0001 | 0.0000 | -1.4679 | 0.1424 |
4.1.1.2 Bird conclusions
Bird communities display a positive richness stability relationship. This relationship is stronger at higher temperatures. Equally, high richness bird communities are more stable at higher temperatures, while low richness bird communities are less stable at higher temperatures.
There is some suggestion that this may be explained by synchrony, but the statistics show no strong associations of synchrony with \(t_{med}\).
4.1.2 Fish
Figure 4.13: Stability-diversity relationship at different temperature levels
Figure 4.14: Stability-temperature relationship at different richness levels
Figure 4.15: Stability-synchrony relationship at different temperature levels
Figure 4.16: Synchrony-temperature relationship (scatterplot)
Figure 4.17: Synchrony-temperature relationship (boxplot)
Figure 4.18: Synchrony richness relationship.
Figure 4.19: Synchrony temperature relationship.
Figure 4.20: Stability - temperature skew relationship.
Figure 4.21: Stability - temperature skew relationship.
Figure 4.22: Stability - temperature skew relationship.
Figure 4.23: Stability - temperature skew relationship.
4.1.2.1 Fish basic statistics
Model of fish stability:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 0.3925 | 0.1402 | 2.7986 | 0.0053 |
| log2(nsp) | 0.0567 | 0.0797 | 0.7109 | 0.4774 |
| t_med_celsius | 0.0270 | 0.0167 | 1.6152 | 0.1068 |
| log2(nsp):t_med_celsius | -0.0105 | 0.0078 | -1.3434 | 0.1797 |
Model of fish synchrony:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | -0.1910 | 0.1212 | -1.5752 | 0.1158 |
| log2(nsp) | -0.3236 | 0.0689 | -4.6968 | 0.0000 |
| t_med_celsius | -0.0293 | 0.0144 | -2.0267 | 0.0432 |
| log2(nsp):t_med_celsius | 0.0075 | 0.0068 | 1.1036 | 0.2702 |
4.1.2.2 Fish conclusions
No significant interaction between richness and temperature for fish.
Figure 4.24: Distribution of temperature trend estimated by non-parametric Sen’s slope, and parametric linear fit slope. Colored points are significant Sen’s slope (green: birds, blue: fish).
##
## Freshwater Terrestrial
## 0.3344828 0.2471910
Figure 4.25: Histogram plot for trends, both taxa.
Figure 4.26: Histogram plot for variability in temperature
Figure 4.27: Histogram plot for variability in temperature
Figure 4.28: Histogram plot for variability in temperature
Figure 4.29: Histogram plot for variability in temperature
4.2 Explanations
So, from the exploratory plots we can see: at higher temperature positive stability-diversity relationship becomes stronger for birds but for fish it becomes weaker. Also fish becomes more asynchronous with increasing temperature. So, why does that happen? to find this we could explore how much the bird species and fish species are consistent to temperature change across all communities.
The cue is: if fish species are not much consistent in their response to warming and vary across sites, that means you cannot make a conclusion that they would become similar with changing temperature. On another note, bird species should be more consistent towards warming if their is no change in their synchrony level across communities. Another possibility could be with changing temperature you might loose some species (its not just number of individuals, it will selectively prefer few species with better fitness), and then the communities will be dominated by few species with similar traits (so increasing synchrony). we will test this below.
From the above plots, we can see birds are showing consistent response-distribution across all temperature change, i.e., in either end of temperature spectrum (low or high end). That’s why the synchrony level remains similar for birds. But for fish, warming increases the richness (addition of new species), and as fish species now become more variable in response to temperature sensitivity (trait-variation), they show more asynchrony compared to low temperature scenario where only few species exists (see smaller circle size on the map for lowT,<50%CI) and show similar traits (so more synchrony). Note: when I show this to Frank, he commented on how much robust is the pattern for fish at low T as there are only few species existed across 145 sites - so it also depends on how we considered the lowT-highT communities. I set beyond 50% CI of temperature range as low/high. Even if I decrease that to 30% CI, still very few species found in low T sites (15 sp across 203 sites: 80% >0, 20% <0 line).
To further explore this idea: we collected traits data for birds and fish species used in the analysis. For fish-traits, I will use body length measurements, for bird-traits I will use HWI (Hand-wing index). From below figures: at high T, birds have slightly less dispersal ability (lower HWI), but richness is more or less uniformly spread at either temperature range. For fish, at lowT, few large species exists with similar traits (remember the previous histogram plot 90-10) showing higher synchrony, as temperature increases addition of new small fishes in the community (maybe better environment for them to exist in that temperature rather than too cold water) makes them asynchronous with more trait variation (histogram plot 66-34).
When I showed this to Blake, he was not convinced by the idea to split the data into two: low/high based on t_med (to him this temperature difference is more on latitudinal differences as shown in the map), and same species can exist in both communities - so why changing t_med should change the synchrony level for fish? and getting different bodysize fish from low/high t_med (fewer big fish in lowT and many smaller fish in highT) is not explaining why big fish should be more synchronous - is it because of fewer species (richness) or because bigger fish abundance change needs more time - not on annual scale?
So, I thought to make a plot of how community-level average response traits (average of standardised correlation between species abundance with t_med timeseries across sites) changes with increasing temperature (t_med)? For fish, it should decrease with increasing t_med, whereas for birds it should be a flat relationship.
Possible explanation:
Figure 4.30: Response variation with temperature
Now, we will do a path analysis for a simplistic mixed effect model to see the environmental effects on community stability for both taxa.
## ============ model summary for birds ===========## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## R 1.88 [1.74, 2.05] 1.37 0.53 [0.49, 0.57]
## E 1.10 [1.05, 1.19] 1.05 0.91 [0.84, 0.95]
## VR 1.91 [1.77, 2.08] 1.38 0.52 [0.48, 0.57]
## A 2.15 [1.98, 2.35] 1.47 0.46 [0.43, 0.50]
## t_med_celsius 1.14 [1.09, 1.23] 1.07 0.88 [0.81, 0.92]
## t.sens.slope.celsius 1.07 [1.03, 1.17] 1.04 0.93 [0.85, 0.97]
## t_skw_celsius 1.03 [1.00, 1.22] 1.01 0.97 [0.82, 1.00]
## t_varIQR_celsius 1.11 [1.06, 1.20] 1.05 0.90 [0.83, 0.95]##
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##
## Structural Equation Model of psem_birds$model_psem
##
## Call:
## A ~ R + E + VR + MedianT + VarT + TrendT + SkewT
## VR ~ R + E + MedianT + VarT + TrendT
## R ~ MedianT + VarT + TrendT
## E ~ R + MedianT + VarT + TrendT
## stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + SkewT
##
## AIC
## 13982.614
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## R ~ SkewT + ... coef 1237.784 0.0534 0.8173
## E ~ SkewT + ... coef 1239.821 3.2520 0.0716
## VR ~ SkewT + ... coef 937.269 0.2742 0.6006
##
## --
## Global goodness-of-fit:
##
## Chi-Squared = NA with P-value = NA and on 3 degrees of freedom
## Fisher's C = 6.697 with P-value = 0.35 and on 6 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value
## A R 0.7455 0.0222 446.3098 1111.4656 0.0000
## A E 0.1624 0.0212 700.9222 57.8476 0.0000
## A VR 0.6063 0.0209 1184.5456 839.6357 0.0000
## A MedianT -0.0085 0.0259 164.4514 0.1058 0.7454
## A VarT 0.0529 0.0233 700.1938 5.1095 0.0241
## A TrendT 0.0173 0.0237 300.5050 0.5238 0.4698
## A SkewT -0.0512 0.0207 442.1973 6.0023 0.0147
## VR R -0.3076 0.0321 832.6035 90.6595 0.0000
## VR E -0.2165 0.0299 1060.2572 52.1107 0.0000
## VR MedianT -0.0022 0.0457 228.2758 0.0023 0.9619
## VR VarT -0.0688 0.0338 1035.7142 4.1150 0.0428
## VR TrendT -0.0335 0.0375 599.1077 0.7868 0.3754
## R MedianT -0.0310 0.0516 693.6981 0.3563 0.5507
## R VarT 0.0236 0.0291 1238.6214 0.6521 0.4195
## R TrendT -0.0012 0.0345 1230.3185 0.0011 0.9730
## E R -0.0800 0.0313 1234.0487 6.5225 0.0108
## E MedianT 0.1189 0.0549 545.3556 4.6386 0.0317
## E VarT 0.0163 0.0322 1240.9500 0.2548 0.6138
## E TrendT 0.0834 0.0379 1188.0874 4.8253 0.0282
## stability R 0.1308 0.0318 1104.6547 16.7942 0.0000
## stability E -0.0510 0.0225 1094.9592 5.1143 0.0239
## stability VR -0.6950 0.0270 1227.0471 662.4722 0.0000
## stability A -0.1304 0.0275 1220.2194 22.3790 0.0000
## stability MedianT -0.0025 0.0374 265.5627 0.0044 0.9471
## stability VarT -0.0192 0.0245 1001.6151 0.6107 0.4347
## stability TrendT 0.0314 0.0277 628.5534 1.2779 0.2587
## stability SkewT 0.0116 0.0225 892.4499 0.2633 0.6080
## stability R:MedianT 0.0423 0.0229 758.5298 3.3823 0.0663
## Std.Estimate
## 0.7455 ***
## 0.1624 ***
## 0.6063 ***
## -0.0085
## 0.0529 *
## 0.0173
## -0.0512 *
## -0.3076 ***
## -0.2165 ***
## -0.0022
## -0.0688 *
## -0.0335
## -0.0310
## 0.0236
## -0.0012
## -0.0800 *
## 0.1189 *
## 0.0163
## 0.0834 *
## 0.1308 ***
## -0.0510 *
## -0.6950 ***
## -0.1304 ***
## -0.0025
## -0.0192
## 0.0314
## 0.0116
## 0.0481
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method Marginal Conditional
## A none 0.59 0.60
## VR none 0.15 0.32
## R none 0.00 0.65
## E none 0.03 0.57
## stability none 0.57 0.65## ============ model summary for fish ===========## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## R 3.00 [2.64, 3.44] 1.73 0.33 [0.29, 0.38]
## E 1.26 [1.16, 1.42] 1.12 0.79 [0.71, 0.86]
## VR 1.30 [1.19, 1.46] 1.14 0.77 [0.69, 0.84]
## A 2.42 [2.15, 2.76] 1.56 0.41 [0.36, 0.47]
## t_med_celsius 1.44 [1.32, 1.62] 1.20 0.69 [0.62, 0.76]
## t.sens.slope.celsius 1.15 [1.08, 1.30] 1.07 0.87 [0.77, 0.93]
## t_skw_celsius 1.22 [1.13, 1.37] 1.11 0.82 [0.73, 0.88]
## t_varIQR_celsius 1.43 [1.31, 1.61] 1.20 0.70 [0.62, 0.77]##
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##
## Structural Equation Model of psem_fish$model_psem
##
## Call:
## A ~ R + E + VR + MedianT + VarT + TrendT + SkewT
## VR ~ R + E + MedianT + VarT + TrendT
## R ~ MedianT + VarT + TrendT
## E ~ R + MedianT + VarT + TrendT
## stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + SkewT
##
## AIC
## 6146.839
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## R ~ SkewT + ... coef 456.9584 0.5157 0.4730
## E ~ SkewT + ... coef 306.8676 2.9680 0.0859
## VR ~ SkewT + ... coef 270.2988 2.9794 0.0855
##
## --
## Global goodness-of-fit:
##
## Chi-Squared = NA with P-value = NA and on 3 degrees of freedom
## Fisher's C = 11.325 with P-value = 0.079 and on 6 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value
## A R 1.0012 0.0328 62.9350 847.8942 0.0000
## A E 0.1136 0.0236 346.7961 22.4552 0.0000
## A VR 0.1119 0.0241 496.7346 21.1484 0.0000
## A MedianT -0.0860 0.0299 56.9548 7.9227 0.0067
## A VarT 0.0346 0.0296 200.1121 1.3228 0.2515
## A TrendT 0.0148 0.0228 280.4936 0.4090 0.5230
## A SkewT -0.0179 0.0273 175.9412 0.4189 0.5183
## VR R -0.5555 0.0617 423.3584 79.4244 0.0000
## VR E -0.2990 0.0403 570.2196 54.5028 0.0000
## VR MedianT -0.3011 0.0602 118.4350 24.6125 0.0000
## VR VarT -0.0370 0.0526 310.4732 0.4841 0.4871
## VR TrendT 0.0748 0.0420 448.8656 3.1242 0.0778
## R MedianT 0.2288 0.0518 181.7185 19.2135 0.0000
## R VarT 0.1965 0.0376 536.5141 27.0185 0.0000
## R TrendT -0.0560 0.0292 575.9680 3.6527 0.0565
## E R -0.4090 0.0625 483.2365 42.1907 0.0000
## E MedianT -0.1701 0.0656 131.6147 6.6184 0.0112
## E VarT -0.1013 0.0556 370.9077 3.2638 0.0716
## E TrendT 0.0693 0.0439 497.6634 2.4564 0.1177
## stability R -0.2460 0.1089 558.8370 5.0659 0.0248
## stability E -0.2240 0.0424 562.9324 27.7165 0.0000
## stability VR -0.5537 0.0416 557.8549 176.5603 0.0000
## stability A 0.1769 0.0681 542.4500 6.7309 0.0097
## stability MedianT -0.1215 0.0790 199.7818 2.3381 0.1278
## stability VarT -0.1911 0.0586 547.0224 10.5223 0.0013
## stability TrendT -0.0125 0.0433 563.4716 0.0827 0.7738
## stability SkewT -0.1347 0.0586 398.7438 5.2196 0.0229
## stability R:MedianT -0.0669 0.0630 569.2542 1.1224 0.2898
## Std.Estimate
## 1.0012 ***
## 0.1136 ***
## 0.1119 ***
## -0.0860 **
## 0.0346
## 0.0148
## -0.0179
## -0.5555 ***
## -0.2990 ***
## -0.3011 ***
## -0.0370
## 0.0748
## 0.2288 ***
## 0.1965 ***
## -0.0560
## -0.4090 ***
## -0.1701 *
## -0.1013
## 0.0693
## -0.2460 *
## -0.2240 ***
## -0.5537 ***
## 0.1769 **
## -0.1215
## -0.1911 **
## -0.0125
## -0.1347 *
## -0.0576
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method Marginal Conditional
## A none 0.78 0.78
## VR none 0.39 0.50
## R none 0.15 0.55
## E none 0.27 0.44
## stability none 0.24 0.52## ============ model summary for fish subset ===========## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## R 3.14 [2.67, 3.75] 1.77 0.32 [0.27, 0.37]
## E 1.20 [1.10, 1.40] 1.09 0.83 [0.71, 0.91]
## VR 1.27 [1.15, 1.48] 1.13 0.79 [0.68, 0.87]
## A 2.51 [2.16, 2.98] 1.59 0.40 [0.34, 0.46]
## t_med_celsius 1.53 [1.36, 1.78] 1.24 0.65 [0.56, 0.74]
## t.sens.slope.celsius 1.17 [1.08, 1.38] 1.08 0.85 [0.73, 0.93]
## t_skw_celsius 1.30 [1.17, 1.51] 1.14 0.77 [0.66, 0.85]
## t_varIQR_celsius 1.64 [1.45, 1.91] 1.28 0.61 [0.52, 0.69]##
|
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|
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|
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##
## Structural Equation Model of psem_fish$model_psem
##
## Call:
## A ~ R + E + VR + MedianT + VarT + TrendT + SkewT
## VR ~ R + E + MedianT + VarT + TrendT
## R ~ MedianT + VarT + TrendT
## E ~ R + MedianT + VarT + TrendT
## stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + SkewT
##
## AIC
## 3842.186
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## R ~ SkewT + ... coef 218.4151 0.0025 0.9603
## E ~ SkewT + ... coef 222.4839 0.6325 0.4273
## VR ~ SkewT + ... coef 160.7222 1.9303 0.1666
##
## --
## Global goodness-of-fit:
##
## Chi-Squared = NA with P-value = NA and on 3 degrees of freedom
## Fisher's C = 5.366 with P-value = 0.498 and on 6 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value
## A R 0.9888 0.0393 17.6050 474.4369 0.0000
## A E 0.1051 0.0294 160.3627 11.9838 0.0007
## A VR 0.1186 0.0312 244.7211 13.6091 0.0003
## A MedianT -0.0959 0.0369 36.1582 6.3364 0.0164
## A VarT 0.0487 0.0407 71.4778 1.3333 0.2521
## A TrendT -0.0030 0.0303 202.4271 0.0096 0.9219
## A SkewT 0.0017 0.0366 86.5560 0.0021 0.9636
## VR R -0.5611 0.0751 309.8607 54.4328 0.0000
## VR E -0.1754 0.0526 328.0494 10.9485 0.0010
## VR MedianT -0.2488 0.0743 83.1989 10.9515 0.0014
## VR VarT -0.0472 0.0729 147.4927 0.4057 0.5251
## VR TrendT 0.1521 0.0533 287.9211 7.9813 0.0051
## R MedianT 0.2569 0.0616 98.2880 17.0351 0.0001
## R VarT 0.2858 0.0559 230.1676 25.5485 0.0000
## R TrendT -0.0549 0.0401 342.5768 1.8492 0.1748
## E R -0.4247 0.0729 350.7145 33.5433 0.0000
## E MedianT -0.1340 0.0878 117.1309 2.2876 0.1331
## E VarT -0.1265 0.0799 247.8168 2.4534 0.1185
## E TrendT 0.0248 0.0551 342.9323 0.2007 0.6544
## stability R -0.0912 0.1209 345.8177 0.5641 0.4531
## stability E -0.1287 0.0520 341.0703 6.0766 0.0142
## stability VR -0.5490 0.0505 329.5510 117.5795 0.0000
## stability A 0.1312 0.0782 310.1591 2.8026 0.0951
## stability MedianT -0.1981 0.1022 177.9536 3.7111 0.0556
## stability VarT -0.2216 0.0859 333.5485 6.5560 0.0109
## stability TrendT 0.0034 0.0538 345.4809 0.0038 0.9506
## stability SkewT -0.0873 0.0818 268.9923 1.1212 0.2906
## stability R:MedianT -0.1069 0.0788 343.8199 1.8335 0.1766
## Std.Estimate
## 0.9888 ***
## 0.1051 ***
## 0.1186 ***
## -0.0959 *
## 0.0487
## -0.0030
## 0.0017
## -0.5611 ***
## -0.1754 **
## -0.2488 **
## -0.0472
## 0.1521 **
## 0.2569 ***
## 0.2858 ***
## -0.0549
## -0.4247 ***
## -0.1340
## -0.1265
## 0.0248
## -0.0912
## -0.1287 *
## -0.5490 ***
## 0.1312
## -0.1981
## -0.2216 *
## 0.0034
## -0.0873
## -0.0743
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method Marginal Conditional
## A none 0.77 0.77
## VR none 0.37 0.50
## R none 0.22 0.52
## E none 0.26 0.56
## stability none 0.22 0.64## ============ model summary for birds ===========## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## R 1.87 [1.73, 2.04] 1.37 0.53 [0.49, 0.58]
## E 1.10 [1.05, 1.19] 1.05 0.91 [0.84, 0.95]
## VR 1.91 [1.76, 2.08] 1.38 0.52 [0.48, 0.57]
## A 2.14 [1.97, 2.33] 1.46 0.47 [0.43, 0.51]
## t_med_celsius 1.13 [1.08, 1.22] 1.06 0.88 [0.82, 0.93]
## t.sens.slope.celsius 1.06 [1.02, 1.17] 1.03 0.95 [0.86, 0.98]
## t_kurt_celsius 1.19 [1.13, 1.28] 1.09 0.84 [0.78, 0.89]
## t_varIQR_celsius 1.30 [1.22, 1.40] 1.14 0.77 [0.71, 0.82]##
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|
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##
## Structural Equation Model of psem_birds$model_psem
##
## Call:
## A ~ R + E + VR + MedianT + VarT + TrendT + KurtT
## VR ~ R + E + MedianT + VarT + TrendT
## R ~ MedianT + VarT + TrendT
## E ~ R + MedianT + VarT + TrendT + KurtT
## stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + KurtT
##
## AIC
## 13988.537
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## R ~ KurtT + ... coef 1229.173 0.334 0.5634
## VR ~ KurtT + ... coef 1074.700 0.048 0.8266
##
## --
## Global goodness-of-fit:
##
## Chi-Squared = NA with P-value = NA and on 2 degrees of freedom
## Fisher's C = 1.528 with P-value = 0.822 and on 4 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value
## A R 0.7490 0.0221 447.1684 1134.6897 0.0000
## A E 0.1627 0.0211 660.8626 58.5169 0.0000
## A VR 0.6054 0.0209 1182.3204 836.5760 0.0000
## A MedianT 0.0055 0.0253 163.1374 0.0471 0.8285
## A VarT 0.0655 0.0257 813.7156 6.4313 0.0114
## A TrendT 0.0117 0.0233 300.0538 0.2495 0.6178
## A KurtT 0.0172 0.0227 530.3014 0.5640 0.4530
## VR R -0.3076 0.0321 832.6035 90.6595 0.0000
## VR E -0.2165 0.0299 1060.2572 52.1107 0.0000
## VR MedianT -0.0022 0.0457 228.2758 0.0023 0.9619
## VR VarT -0.0688 0.0338 1035.7142 4.1150 0.0428
## VR TrendT -0.0335 0.0375 599.1077 0.7868 0.3754
## R MedianT -0.0310 0.0516 693.6981 0.3563 0.5507
## R VarT 0.0236 0.0291 1238.6214 0.6521 0.4195
## R TrendT -0.0012 0.0345 1230.3185 0.0011 0.9730
## E R -0.0793 0.0312 1233.5632 6.4278 0.0114
## E MedianT 0.1267 0.0550 543.4833 5.2528 0.0223
## E VarT -0.0126 0.0343 1237.8231 0.1346 0.7137
## E TrendT 0.0754 0.0379 1183.2429 3.9247 0.0478
## E KurtT -0.0769 0.0314 1237.2402 5.9692 0.0147
## stability R 0.1315 0.0318 1119.1701 16.9841 0.0000
## stability E -0.0495 0.0225 1102.5970 4.7975 0.0287
## stability VR -0.6952 0.0269 1227.7151 663.7277 0.0000
## stability A -0.1310 0.0275 1219.4755 22.7557 0.0000
## stability MedianT -0.0037 0.0375 263.5502 0.0094 0.9228
## stability VarT -0.0112 0.0266 1136.0895 0.1762 0.6747
## stability TrendT 0.0341 0.0275 640.8536 1.5224 0.2177
## stability KurtT 0.0189 0.0242 1038.8229 0.6057 0.4366
## stability R:MedianT 0.0416 0.0229 759.8032 3.2678 0.0710
## Std.Estimate
## 0.7490 ***
## 0.1627 ***
## 0.6054 ***
## 0.0055
## 0.0655 *
## 0.0117
## 0.0172
## -0.3076 ***
## -0.2165 ***
## -0.0022
## -0.0688 *
## -0.0335
## -0.0310
## 0.0236
## -0.0012
## -0.0793 *
## 0.1267 *
## -0.0126
## 0.0754 *
## -0.0769 *
## 0.1315 ***
## -0.0495 *
## -0.6952 ***
## -0.1310 ***
## -0.0037
## -0.0112
## 0.0341
## 0.0189
## 0.0474
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method Marginal Conditional
## A none 0.58 0.59
## VR none 0.15 0.32
## R none 0.00 0.65
## E none 0.03 0.58
## stability none 0.57 0.65## ============ model summary for fish ===========## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## R 3.24 [2.84, 3.72] 1.80 0.31 [0.27, 0.35]
## E 1.28 [1.18, 1.43] 1.13 0.78 [0.70, 0.85]
## VR 1.31 [1.21, 1.47] 1.15 0.76 [0.68, 0.83]
## A 2.59 [2.29, 2.97] 1.61 0.39 [0.34, 0.44]
## t_med_celsius 1.48 [1.35, 1.67] 1.22 0.67 [0.60, 0.74]
## t.sens.slope.celsius 1.15 [1.08, 1.30] 1.07 0.87 [0.77, 0.93]
## t_kurt_celsius 1.29 [1.19, 1.45] 1.14 0.77 [0.69, 0.84]
## t_varIQR_celsius 1.50 [1.36, 1.69] 1.23 0.67 [0.59, 0.73]##
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##
## Structural Equation Model of psem_fish$model_psem
##
## Call:
## A ~ R + E + VR + MedianT + VarT + TrendT + KurtT
## VR ~ R + E + MedianT + VarT + TrendT
## R ~ MedianT + VarT + TrendT
## E ~ R + MedianT + VarT + TrendT + KurtT
## stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + KurtT
##
## AIC
## 6048.136
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## R ~ KurtT + ... coef 474.4466 0.8827 0.3479
## VR ~ KurtT + ... coef 293.0998 4.3328 0.0383 *
##
## --
## Global goodness-of-fit:
##
## Chi-Squared = 78.585 with P-value = 0 and on 2 degrees of freedom
## Fisher's C = 8.639 with P-value = 0.071 and on 4 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value
## A R 1.0784 0.0353 93.1919 867.0076 0.0000
## A E 0.1208 0.0234 409.1075 25.9621 0.0000
## A VR 0.1204 0.0238 521.8463 25.3079 0.0000
## A MedianT -0.1053 0.0307 56.0372 11.2763 0.0014
## A VarT 0.0147 0.0293 171.8530 0.2418 0.6236
## A TrendT 0.0198 0.0224 265.2202 0.7606 0.3839
## A KurtT 0.0111 0.0253 181.9446 0.1870 0.6659
## VR R -0.5555 0.0617 423.3584 79.4244 0.0000
## VR E -0.2990 0.0403 570.2196 54.5028 0.0000
## VR MedianT -0.3011 0.0602 118.4350 24.6125 0.0000
## VR VarT -0.0370 0.0526 310.4732 0.4841 0.4871
## VR TrendT 0.0748 0.0420 448.8656 3.1242 0.0778
## R MedianT 0.2288 0.0518 181.7185 19.2135 0.0000
## R VarT 0.1965 0.0376 536.5141 27.0185 0.0000
## R TrendT -0.0560 0.0292 575.9680 3.6527 0.0565
## E R -0.4290 0.0662 489.1821 41.2864 0.0000
## E MedianT -0.1931 0.0742 138.3461 6.6402 0.0110
## E VarT -0.1070 0.0605 410.2830 3.0749 0.0803
## E TrendT 0.0768 0.0443 490.1647 2.9560 0.0862
## E KurtT -0.0181 0.0528 354.4215 0.1156 0.7340
## stability R -0.2463 0.1196 558.9948 4.2128 0.0406
## stability E -0.2214 0.0430 554.5971 26.3797 0.0000
## stability VR -0.5498 0.0422 547.7665 169.2165 0.0000
## stability A 0.1828 0.0710 520.0110 6.6113 0.0104
## stability MedianT -0.1430 0.0787 170.6970 3.2606 0.0727
## stability VarT -0.1992 0.0596 485.6580 11.0336 0.0010
## stability TrendT -0.0150 0.0433 537.6676 0.1184 0.7309
## stability KurtT 0.0898 0.0522 430.7731 2.9168 0.0884
## stability R:MedianT -0.1102 0.0645 558.9765 2.9105 0.0886
## Std.Estimate
## 1.0784 ***
## 0.1208 ***
## 0.1204 ***
## -0.1053 **
## 0.0147
## 0.0198
## 0.0111
## -0.5555 ***
## -0.2990 ***
## -0.3011 ***
## -0.0370
## 0.0748
## 0.2288 ***
## 0.1965 ***
## -0.0560
## -0.4290 ***
## -0.1931 *
## -0.1070
## 0.0768
## -0.0181
## -0.2463 *
## -0.2214 ***
## -0.5498 ***
## 0.1828 *
## -0.1430
## -0.1992 ***
## -0.0150
## 0.0898
## -0.0948
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method Marginal Conditional
## A none 0.80 0.81
## VR none 0.39 0.50
## R none 0.15 0.55
## E none 0.29 0.45
## stability none 0.25 0.49## ============ model summary for fish subset ===========## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## R 3.34 [2.83, 4.00] 1.83 0.30 [0.25, 0.35]
## E 1.21 [1.11, 1.42] 1.10 0.83 [0.70, 0.90]
## VR 1.28 [1.16, 1.49] 1.13 0.78 [0.67, 0.87]
## A 2.66 [2.28, 3.17] 1.63 0.38 [0.32, 0.44]
## t_med_celsius 1.52 [1.35, 1.77] 1.23 0.66 [0.56, 0.74]
## t.sens.slope.celsius 1.16 [1.07, 1.37] 1.08 0.86 [0.73, 0.94]
## t_kurt_celsius 1.32 [1.19, 1.54] 1.15 0.76 [0.65, 0.84]
## t_varIQR_celsius 1.70 [1.49, 1.99] 1.30 0.59 [0.50, 0.67]##
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|
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##
## Structural Equation Model of psem_fish$model_psem
##
## Call:
## A ~ R + E + VR + MedianT + VarT + TrendT + KurtT
## VR ~ R + E + MedianT + VarT + TrendT
## R ~ MedianT + VarT + TrendT
## E ~ R + MedianT + VarT + TrendT + KurtT
## stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + KurtT
##
## AIC
## 3767.796
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## R ~ KurtT + ... coef 247.2314 2.0192 0.1566
## VR ~ KurtT + ... coef 182.3856 2.7137 0.1012
##
## --
## Global goodness-of-fit:
##
## Chi-Squared = 55.646 with P-value = 0 and on 2 degrees of freedom
## Fisher's C = 8.289 with P-value = 0.082 and on 4 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value
## A R 1.0407 0.0398 14.1819 503.7682 0.0000
## A E 0.1142 0.0287 142.3959 14.7831 0.0002
## A VR 0.1295 0.0307 228.4381 16.7192 0.0001
## A MedianT -0.1120 0.0346 27.4854 9.7957 0.0041
## A VarT 0.0317 0.0374 40.9766 0.6483 0.4254
## A TrendT -0.0095 0.0288 151.8061 0.1033 0.7484
## A KurtT -0.0055 0.0321 71.2760 0.0274 0.8690
## VR R -0.5611 0.0751 309.8607 54.4328 0.0000
## VR E -0.1754 0.0526 328.0494 10.9485 0.0010
## VR MedianT -0.2488 0.0743 83.1989 10.9515 0.0014
## VR VarT -0.0472 0.0729 147.4927 0.4057 0.5251
## VR TrendT 0.1521 0.0533 287.9211 7.9813 0.0051
## R MedianT 0.2569 0.0616 98.2880 17.0351 0.0001
## R VarT 0.2858 0.0559 230.1676 25.5485 0.0000
## R TrendT -0.0549 0.0401 342.5768 1.8492 0.1748
## E R -0.4413 0.0766 335.3222 32.8430 0.0000
## E MedianT -0.1902 0.0998 140.7310 3.5446 0.0618
## E VarT -0.1707 0.0890 262.2840 3.6034 0.0588
## E TrendT 0.0417 0.0560 334.9250 0.5493 0.4591
## E KurtT -0.0880 0.0715 283.2761 1.4858 0.2239
## stability R -0.0513 0.1305 320.9321 0.1533 0.6957
## stability E -0.1169 0.0525 332.6805 4.9057 0.0274
## stability VR -0.5396 0.0509 319.8274 111.7596 0.0000
## stability A 0.1177 0.0808 286.8070 2.1163 0.1468
## stability MedianT -0.2691 0.1013 172.9798 6.9598 0.0091
## stability VarT -0.2583 0.0868 302.3396 8.7024 0.0034
## stability TrendT -0.0060 0.0538 336.9948 0.0122 0.9121
## stability KurtT -0.0066 0.0692 315.7991 0.0089 0.9250
## stability R:MedianT -0.1391 0.0800 335.7542 3.0082 0.0838
## Std.Estimate
## 1.0407 ***
## 0.1142 ***
## 0.1295 ***
## -0.1120 **
## 0.0317
## -0.0095
## -0.0055
## -0.5611 ***
## -0.1754 **
## -0.2488 **
## -0.0472
## 0.1521 **
## 0.2569 ***
## 0.2858 ***
## -0.0549
## -0.4413 ***
## -0.1902
## -0.1707
## 0.0417
## -0.0880
## -0.0513
## -0.1169 *
## -0.5396 ***
## 0.1177
## -0.2691 **
## -0.2583 **
## -0.0060
## -0.0066
## -0.0966
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method Marginal Conditional
## A none 0.79 0.79
## VR none 0.37 0.50
## R none 0.22 0.52
## E none 0.28 0.57
## stability none 0.23 0.62